Introducción a La Optimización

Texts in Applied Mathematics

46

Editors J.E. Marsden L. Sirovich S.S. Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton

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Pablo Pedregal

Introduction to Optimization

With 41 Illustrations

Pablo Pedregal ETSI Industriales Universidad de Castilla-La Mancha 13071 Ciudad Real Spain pablo.pedregal@uclm.es Series Editors
J.E.Marsden Control and Dynamical Systems, 107–81 California Institute of Technology Pasadena, CA 91125 USA marsden@cds.caltech.edu S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA ssa@math.umd.edu Mathematics Subject Classification (2000): 49-01, 49L20, 90C90, 65K10 L. Sirovich Division of AppliedMathematics Brown University Providence, RI 02912 USA chico@camelot.mssm.edu

Library of Congress Cataloging-in-Publication Data Pedregal, Pablo, 1963– Introduction to optimization / Pablo Pedregal. p. cm. — (Texts in applied mathematics ; 46) Includes bibliographical references and index. ISBN 0-387-40398-1 (acid-free paper) 1. Mathematical optimization. I. Title. II. Series. QA402.5.P4 2003 519.3—dc212003053895 ISBN 0-387-40398-1 Printed on acid-free paper.

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To Daniel, Silvia, Jaime, and Nuria

Series Preface

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring ofboundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newertechniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduatecourses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California Providence, Rhode Island College Park, Maryland J.E. Marsden L. Sirovich S.S. Antman

Preface

This book should serve as an undergraduate text to introduce students of science and engineering to the fascinating field ofoptimization. Several features have been united: conciseness and completeness, brevity and clarity, emphasis on the justification of ideas and techniques and also on applications, etc. One of the novelties of the text is that it ties together fields that are often treated as separate. Indeed, it is hard to find a single textbook where mathematical programming, variational problems, and optimal control problems...